Finite Group Databasebeta

← #13172000

Subgroups — #13172000

Order 1728.

1726 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#626C211yesmaximal, characteristic
2#11723723C211yesmaximal, characteristic, complemented
3C3⋊D3×#217C211yesmaximal, characteristic, complemented
4D3×#3757C211yesmaximal, characteristic, complemented
5#11723594C211yesmaximal, characteristic, complemented
6C3×D3×#217C211yesmaximal, characteristic, complemented
7C3×#63955C211yesmaximal, characteristic, complemented
8#11722929C212yesmaximal, complemented
9#11722928C212yesmaximal, complemented
10#11722927C212yesmaximal, complemented
11Dic3×#626C212yesmaximal, complemented
12#10595506—31nomaximal
13#10594982—31nomaximal
14#10594182—31nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C23×C32×D3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×#6294C2212yescomplemented
19C2×Dic3×C3⋊D3C2212yescomplemented
20C2×D3×C3⋊Dic3C2212yescomplemented
21C2×C3×#626C418yescomplemented
22C2×C3×#626C2211yescharacteristic
23C2×C3×#626C2211yescharacteristic
24C2×C3×#626C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×D3×Dic3C2212yescomplemented
27#88864C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C32×#217C2211yescharacteristic
31#88814C2212yescomplemented
32Dic3⋊(C3⋊Dic3)C2212yescomplemented
33#88803C2212yescomplemented
34(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
35Dic3×C3⋊Dic3C2212yescomplemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C3×Dic32C2212yescomplemented
39C22×C3×#67—31no—
40C22×C3×D12—31no—
41C22×#626D311yescharacteristic
42C2×#3757—31no—
43#64135—31no—
44C22⋊C4×C3⋊D3—31no—
45C2×C3×#217—31no—
46C3×#926—31no—
47C3×D3×C22⋊C4—31no—
48C3×#877—31no—
49#63974—31no—
50#67⋊Dic3—32no—
51#67⋊Dic3—32no—
52Dic3×#67—32no—
53Dic3×#67—32no—
54D3×#217—31no—
55D3×#217—31no—
56D3×#217—31no—
57D3×#217—31no—
58D3×#217—31no—
59D3×#217—31no—
60D3×#217—61no—
61D3×#217—61no—
62D3×#217D311yescharacteristic, complemented
63#63955—31no—
64#63955—31no—
65#63955—61no—
66#63955D311yescharacteristic, complemented
67#63904—32no—
68C4×#626—32no—
69#63898—32no—
70#63898—32no—
71Dic3×D12—32no—
72Dic3×D12—32no—
73#63881—32no—
74#63880—32no—
75C23×C33C2311yescharacteristic
76C22×C3×C3⋊D3—42no—
77C22×C3×C3⋊D3C2×C414yescomplemented
78C22×C3×C3⋊D3C2311yescharacteristic
79C22×C3×C3⋊D3C2311yescharacteristic
80C22×C32×D3—42no—
81C22×C32×D3C2×C414yescomplemented
82C22×C32×D3C2311yescharacteristic
83C22×C32×D3C2311yescharacteristic
84C2×C3⋊(C3⋊Dic3)C2312yes—
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2312yes—
87C2×C32×Dic3C2×C414yescomplemented
88C2×C32×Dic3C2312yes—
89C2×C32×Dic3C2311yescharacteristic
90C2×C32×Dic3C2311yescharacteristic
91#6294—42no—
92Dic3×C3⋊D3—42no—
93D3×C3⋊Dic3—42no—
94C3×#626C2×C414yescomplemented
95C3×#626C2×C414yescomplemented
96C3×#626C2×C414yescomplemented
97C3×#626C2×C414yescomplemented
98C3×D3×Dic3—42no—
99#5798—91no—
100#5521—91no—
101#5486—91no—
102C24×C32—31no—
103C23×C3⋊D3C2×D311yescharacteristic
104C23×C3×D3—21no—
105C23×C3×D3—31no—
106C23×C3×D3—31no—
107C23×C3×D3—61no—
108C23×C3×D3C2×D311yescharacteristic
109C23×C3×D3C2×D311yescharacteristic
110C22×C32×C4—31no—
111C22×C3⋊Dic3—32no—
112C2×C4×C3⋊D3—32no—
113C2×C3×#67—38no—
114C2×C3×#67—31no—
115C2×C3×#67—31no—
116C2×C3×#67—31no—
117C2×C3×#67—31no—
118C22×C3×Dic3—21no—
119C22×C3×Dic3—32no—
120C22×C3×Dic3C2×D311yescharacteristic
121C22×C3×Dic3C2×D311yescharacteristic
122C2×C3×D12—38no—
123C2×C3×D12—31no—
124C2×C3×D12—31no—
125C2×C3×D12—31no—
126C2×C3×D12—31no—
127C2×C3×C4×D3—32no—
128C2×#626Dic318yescomplemented
129C2×#626C2×D311yescharacteristic
130C2×#626C2×D311yescharacteristic
131C2×#626C2×D311yescharacteristic
132C2×#626C2×D311yescharacteristic
133C2×#624—32no—
134C2×D3×Dic3—32no—
135C2×D3×Dic3—32no—
136C2×D3×Dic3—32no—
137C2×D3×Dic3—32no—
138C2×D3×Dic3—32no—
139C2×D3×Dic3—32no—
140C2×D3×Dic3—62no—
141C2×D3×Dic3—62no—
142C2×D3×Dic3C2×D312yescomplemented
143C32×C22⋊C4—31no—
144#3757—31no—
145#3757—31no—
146#3757—31no—
147#3757—32no—
148#3757—61no—
149#3757—61no—
150#3757—61no—
151#3757—121no—
152#3757C2×D311yescharacteristic
153#3757C2×D311yescharacteristic
154#3752—32no—
155C4⋊(C3⋊Dic3)—32no—
156C4×C3⋊Dic3—32no—
157C3×#217—21no—
158C3×#217—31no—
159C3×#217—31no—
160C3×#217—31no—
161C3×#217—31no—
162C3×#217—32no—
163C3×#217—61no—
164C3×#217—61no—
165C3×#217C2×D311yescharacteristic
166C3×#217C2×D311yescharacteristic
167C3×(C2×D3)⋊C4—32no—
168C3×C4⋊Dic3—32no—
169C3×Dic3⋊C4—32no—
170C3×C4×Dic3—32no—
171C3×C4×Dic3—32no—
172Dic3⋊Dic3—32no—
173Dic3⋊Dic3—32no—
174Dic3⋊Dic3—62no—
175Dic3⋊Dic3C2×D312yescomplemented
176#3722—32no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3—32no—
179(C2×D3)⋊Dic3—32no—
180(C2×D3)⋊Dic3—32no—
181(C2×D3)⋊Dic3—32no—
182(C2×D3)⋊Dic3—32no—
183(C2×D3)⋊Dic3—62no—
184(C2×D3)⋊Dic3—62no—
185(C2×D3)⋊Dic3C2×D312yescomplemented
186Dic32—32no—
187Dic32—32no—
188Dic32—62no—
189Dic32C2×D312yescomplemented
190C22×C33—22no—
191C22×C33C22×C412yes—
192C22×C33C2411yescharacteristic
193C2×C3×C3⋊D3—22no—
194C2×C3×C3⋊D3—22no—
195C2×C3×C3⋊D3—44no—
196C2×C3×C3⋊D3C22×C412yes—
197C2×C3×C3⋊D3C22×C412yes—
198C2×C32×D3—22no—
199C2×C32×D3—22no—
200C2×C32×D3—44no—
201C2×C32×D3C22×C412yes—
202C2×C32×D3C22×C412yes—
203C3⋊(C3⋊Dic3)—22no—
204C3×C3⋊Dic3—22no—
205C3×C3⋊Dic3—22no—
206C32×Dic3—22no—
207C32×Dic3C22×C412yes—
208C32×Dic3C22×C412yes—
209C22×C3×D4—91no—
210C22×#67—31no—
211C22×D12—31no—
212C3×#117—91no—
213C2×C3×C22⋊C4—91no—
214C2×#217—31no—
215C2×#217—91no—
216C2×#217—91no—
217C2×#217—91no—
218C2×#217—91no—
219C2×#217—181no—
220D4×Dic3—92no—
221D4×Dic3—92no—
222D4×Dic3—92no—
223D4×Dic3—92no—
224C4×#67—92no—
225C4×#67—92no—
226#926—31no—
227#926—91no—
228#926—91no—
229#926—181no—
230#893—92no—
231#893—92no—
232#67⋊C4—92no—
233#67⋊C4—92no—
234D3×C22⋊C4—31no—
235D3×C22⋊C4—91no—
236D3×C22⋊C4—91no—
237D3×C22⋊C4—91no—
238D3×C22⋊C4—91no—
239D3×C22⋊C4—91no—
240D3×C22⋊C4—181no—
241#877—31no—
242#877—91no—
243C4×D12—92no—
244C4×D12—92no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—31no—
249C23×C32—31no—
250C23×C32—34no—
251C23×C32—41no—
252C23×C32—122no—
253C23×C32C22×D311yescharacteristic
254C23×C32C22×D311yescharacteristic
255C23×C32C22×D311yescharacteristic
256C22×C3⋊D3—42no—
257C22×C3⋊D3C2×Dic314yescomplemented
258C22×C3⋊D3C22×D311yescharacteristic
259C22×C3⋊D3C22×D311yescharacteristic
260C22×C3×D3—24no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—31no—
264C22×C3×D3—31no—
265C22×C3×D3—31no—
266C22×C3×D3—31no—
267C22×C3×D3—34no—
268C22×C3×D3—34no—
269C22×C3×D3—42no—
270C22×C3×D3—42no—
271C22×C3×D3—44no—
272C22×C3×D3—61no—
273C22×C3×D3—61no—
274C22×C3×D3—64no—
275C22×C3×D3—122no—
276C22×C3×D3—122no—
277C22×C3×D3—124no—
278C22×C3×D3C4×D314yescomplemented
279C22×C3×D3C2×Dic314yescomplemented
280C22×C3×D3C22×D311yescharacteristic
281C22×C3×D3C22×D311yescharacteristic
282C22×C3×D3C22×D311yescharacteristic
283C22×C3×D3C22×D311yescharacteristic
284C2×C32×C4—34no—
285C2×C32×C4—31no—
286C2×C32×C4—31no—
287C2×C32×C4—32no—
288C2×C3⋊Dic3—32no—
289C2×C3⋊Dic3—32no—
290C2×C3⋊Dic3—32no—
291C2×C3⋊Dic3—62no—
292C2×C3⋊Dic3—62no—
293C2×C3⋊Dic3—62no—
294C2×C3⋊Dic3—122no—
295C2×C3⋊Dic3—122no—
296C2×C3⋊Dic3C22×D312yes—
297C2×C3⋊Dic3C22×D312yes—
298C4×C3⋊D3—122no—
299C3×#67—34no—
300C3×#67—34no—
301C3×#67—34no—
302C3×#67—34no—
303C2×C3×Dic3—24no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—32no—
308C2×C3×Dic3—32no—
309C2×C3×Dic3—32no—
310C2×C3×Dic3—32no—
311C2×C3×Dic3—62no—
312C2×C3×Dic3—62no—
313C2×C3×Dic3—122no—
314C2×C3×Dic3C4×D314yescomplemented
315C2×C3×Dic3C2×Dic314yescomplemented
316C2×C3×Dic3C22×D312yes—
317C2×C3×Dic3C22×D312yes—
318C2×C3×Dic3C22×D311yescharacteristic
319C2×C3×Dic3C22×D311yescharacteristic
320C2×C3×Dic3C22×D311yescharacteristic
321C2×C3×Dic3C22×D311yescharacteristic
322C3×D12—34no—
323C3×D12—34no—
324C3×D12—34no—
325C3×D12—34no—
326C3×C4×D3—122no—
327#626C2×Dic314yescomplemented
328#626C2×Dic314yescomplemented
329#626C2×Dic314yescomplemented
330#626C2×Dic314yescomplemented
331#624—122no—
332D3×Dic3—42no—
333D3×Dic3—122no—
334D3×Dic3—122no—
335D3×Dic3—124no—
336D3×Dic3—122no—
337D3×Dic3—122no—
338D3×Dic3—122no—
339D3×Dic3—122no—
340D3×Dic3—124no—
341#518—271noSylow
342C2×C33—22no—
343C2×C33C23×C411yescharacteristic
344C2×C33H(5,𝔽2)12yes—
345C3×C3⋊D3—22no—
346C3×C3⋊D3—22no—
347C32×D3—22no—
348C32×D3—22no—
349C24×C3—31no—
350C24×C3—31no—
351C24×C3—61no—
352C24×C3—91no—
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—61no—
356C23×D3D3211yescharacteristic
357C2×C3×D4—91no—
358C2×C3×D4—91no—
359C2×C3×D4—91no—
360C2×C3×D4—91no—
361C2×C3×D4—98no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—61no—
365C22×C3×C4—92no—
366C2×#67—38no—
367C2×#67—31no—
368C2×#67—31no—
369C2×#67—31no—
370C2×#67—31no—
371C22×Dic3—32no—
372C22×Dic3—92no—
373C22×Dic3—92no—
374C22×Dic3—92no—
375C22×Dic3—92no—
376C22×Dic3—182no—
377C22×Dic3D3211yescharacteristic
378C2×D12—38no—
379C2×D12—31no—
380C2×D12—31no—
381C2×D12—31no—
382C2×D12—31no—
383C2×C4×D3—32no—
384C2×C4×D3—92no—
385C2×C4×D3—92no—
386C2×C4×D3—92no—
387C2×C4×D3—92no—
388C2×C4×D3—92no—
389C2×C4×D3—182no—
390C3×C4⋊C4—92no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—92no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C42—92no—
398#217—31no—
399#217—31no—
400#217—31no—
401#217—31no—
402#217—32no—
403#217—61no—
404#217—61no—
405#217—92no—
406#217—92no—
407#217—92no—
408#217—91no—
409#217—91no—
410#217—91no—
411#217—92no—
412#217—182no—
413#217—181no—
414#217—181no—
415#217—181no—
416#217—361no—
417#217D3211yescharacteristic
418(C2×D3)⋊C4—32no—
419(C2×D3)⋊C4—92no—
420(C2×D3)⋊C4—92no—
421(C2×D3)⋊C4—92no—
422(C2×D3)⋊C4—92no—
423(C2×D3)⋊C4—92no—
424(C2×D3)⋊C4—182no—
425C4⋊Dic3—32no—
426C4⋊Dic3—92no—
427C4⋊Dic3—92no—
428C4⋊Dic3—182no—
429Dic3⋊C4—32no—
430Dic3⋊C4—92no—
431C4×Dic3—32no—
432C4×Dic3—32no—
433C4×Dic3—92no—
434C4×Dic3—92no—
435C4×Dic3—92no—
436C4×Dic3—182no—
437C22×C32—22no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—32no—
447C22×C32—32no—
448C22×C32—41no—
449C22×C32—42no—
450C22×C32—42no—
451C22×C32—42no—
452C22×C32—42no—
453C22×C32—62no—
454C22×C32—62no—
455C22×C32—82no—
456C22×C32—124no—
457C22×C32C2×C4×D312yes—
458C22×C32C2×C4×D312yes—
459C22×C32C22×Dic312yes—
460C22×C32C23×D311yescharacteristic
461C22×C32C23×D311yescharacteristic
462C22×C32C23×D311yescharacteristic
463C2×C3⋊D3—22no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—44no—
466C2×C3⋊D3C22×Dic312yes—
467C2×C3⋊D3C22×Dic312yes—
468C2×C3×D3—24no—
469C2×C3×D3—22no—
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—32no—
476C2×C3×D3—32no—
477C2×C3×D3—32no—
478C2×C3×D3—32no—
479C2×C3×D3—42no—
480C2×C3×D3—44no—
481C2×C3×D3—44no—
482C2×C3×D3—48no—
483C2×C3×D3—62no—
484C2×C3×D3—62no—
485C2×C3×D3—64no—
486C2×C3×D3—62no—
487C2×C3×D3—62no—
488C2×C3×D3—62no—
489C2×C3×D3—62no—
490C2×C3×D3—122no—
491C2×C3×D3—124no—
492C2×C3×D3—124no—
493C2×C3×D3—128no—
494C2×C3×D3C2×C4×D312yes—
495C2×C3×D3C2×C4×D312yes—
496C2×C3×D3C22×Dic312yes—
497C2×C3×D3C22×Dic312yes—
498C32×C4—32no—
499C32×C4—32no—
500C32×C4—62no—
501C3⋊Dic3—22no—
502C3⋊Dic3—22no—
503C3⋊Dic3—62no—
504C3⋊Dic3—62no—
505C3⋊Dic3—62no—
506C3⋊Dic3—122no—
507C3⋊Dic3—122no—
508C3⋊Dic3—122no—
509C3⋊Dic3—242no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—22no—
514C3×Dic3—42no—
515C3×Dic3—62no—
516C3×Dic3—62no—
517C3×Dic3—62no—
518C3×Dic3—62no—
519C3×Dic3—122no—
520C3×Dic3—122no—
521C3×Dic3C2×C4×D312yes—
522C3×Dic3C2×C4×D312yes—
523C3×Dic3C22×Dic312yes—
524C3×Dic3C22×Dic312yes—
525C22×D4—91no—
526C4×D4—272no—
527C4×D4—272no—
528C4×D4—272no—
529C4×D4—272no—
530#117—91no—
531#117—271no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—271no—
534C2×C22⋊C4—271no—
535C2×C22⋊C4—271no—
536C33#51811yescharacteristic, complemented, Sylow
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—31no—
542C23×C3—31no—
543C23×C3—31no—
544C23×C3—34no—
545C23×C3—34no—
546C23×C3—41no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—64no—
550C23×C3—91no—
551C23×C3—91no—
552C23×C3—94no—
553C23×C3—122no—
554C23×C3—122no—
555C23×C3—124no—
556C23×C3—362no—
557C23×C3C2×D3211yescharacteristic
558C23×C3C2×D3211yescharacteristic
559C23×C3C2×D3211yescharacteristic
560C22×D3—31no—
561C22×D3—31no—
562C22×D3—31no—
563C22×D3—31no—
564C22×D3—34no—
565C22×D3—34no—
566C22×D3—42no—
567C22×D3—61no—
568C22×D3—64no—
569C22×D3—61no—
570C22×D3—122no—
571C22×D3—122no—
572C22×D3—124no—
573C22×D3D3×Dic314yescomplemented
574C22×D3C2×D3211yescharacteristic
575C22×D3C2×D3211yescharacteristic
576C3×D4—94no—
577C3×D4—94no—
578C3×D4—94no—
579C3×D4—94no—
580C2×C3×C4—31no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—34no—
585C2×C3×C4—34no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—64no—
591C2×C3×C4—62no—
592C2×C3×C4—92no—
593C2×C3×C4—92no—
594C2×C3×C4—362no—
595#67—34no—
596#67—34no—
597#67—34no—
598#67—34no—
599C2×Dic3—32no—
600C2×Dic3—32no—
601C2×Dic3—32no—
602C2×Dic3—32no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—92no—
606C2×Dic3—92no—
607C2×Dic3—92no—
608C2×Dic3—122no—
609C2×Dic3—182no—
610C2×Dic3—182no—
611C2×Dic3—182no—
612C2×Dic3—362no—
613C2×Dic3—362no—
614C2×Dic3—362no—
615C2×Dic3—362no—
616C2×Dic3—362no—
617C2×Dic3—364no—
618C2×Dic3D3×Dic314yescomplemented
619C2×Dic3C2×D3212yes—
620C2×Dic3C2×D3211yescharacteristic
621C2×Dic3C2×D3211yescharacteristic
622D12—34no—
623D12—34no—
624D12—34no—
625D12—34no—
626C4×D3—122no—
627C4×D3—362no—
628C4×D3—362no—
629C4×D3—362no—
630C4×D3—362no—
631C4×D3—362no—
632C4×D3—364no—
633C2×C32—22no—
634C2×C32—22no—
635C2×C32—22no—
636C2×C32—21no—
637C2×C32—22no—
638C2×C32—22no—
639C2×C32—21no—
640C2×C32—21no—
641C2×C32—22no—
642C2×C32—41no—
643C2×C32—42no—
644C2×C32—42no—
645C2×C32—42no—
646C2×C32—42no—
647C2×C32—62no—
648C2×C32—62no—
649C2×C32—82no—
650C2×C32C22×C4×D311yescharacteristic
651C2×C32C22×C4×D311yescharacteristic
652C2×C32#100412yes—
653C2×C32#100412yes—
654C2×C32#100912yes—
655C2×C32C23×Dic311yescharacteristic
656C3⋊D3—22no—
657C3⋊D3—22no—
658C3×D3—24no—
659C3×D3—22no—
660C3×D3—22no—
661C3×D3—22no—
662C3×D3—22no—
663C3×D3—42no—
664C3×D3—64no—
665C3×D3—62no—
666C3×D3—62no—
667C3×D3—62no—
668C3×D3—62no—
669C3×D3—122no—
670C24—31no—
671C24—91no—
672C2×D4—91no—
673C2×D4—91no—
674C2×D4—91no—
675C2×D4—91no—
676C2×D4—98no—
677C22×C4—31no—
678C22×C4—92no—
679C22×C4—272no—
680C22×C4—272no—
681C22×C4—272no—
682C4⋊C4—92no—
683C4⋊C4—272no—
684C22⋊C4—31no—
685C22⋊C4—92no—
686C22⋊C4—91no—
687C22⋊C4—91no—
688C22⋊C4—272no—
689C22⋊C4—272no—
690C22⋊C4—272no—
691C22⋊C4—271no—
692C42—92no—
693C42—272no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—32no—
704C22×C3—32no—
705C22×C3—32no—
706C22×C3—32no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—41no—
711C22×C3—42no—
712C22×C3—62no—
713C22×C3—62no—
714C22×C3—64no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—62no—
718C22×C3—62no—
719C22×C3—82no—
720C22×C3—92no—
721C22×C3—92no—
722C22×C3—122no—
723C22×C3—124no—
724C22×C3—124no—
725C22×C3—128no—
726C22×C3—182no—
727C22×C3—182no—
728C22×C3—364no—
729C22×C3C4×D3212yes—
730C22×C3C2×D3×Dic312yes—
731C22×C3C2×D3×Dic312yes—
732C22×C3C22×D3211yescharacteristic
733C22×C3C22×D3211yescharacteristic
734C22×C3C22×D3211yescharacteristic
735C2×D3—22no—
736C2×D3—22no—
737C2×D3—32no—
738C2×D3—32no—
739C2×D3—32no—
740C2×D3—32no—
741C2×D3—44no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—64no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—122no—
750C2×D3—124no—
751C2×D3—124no—
752C2×D3—128no—
753C2×D3C2×D3×Dic312yes—
754C2×D3C2×D3×Dic312yes—
755C3×C4—32no—
756C3×C4—32no—
757C3×C4—32no—
758C3×C4—32no—
759C3×C4—62no—
760C3×C4—62no—
761C3×C4—62no—
762C3×C4—62no—
763C3×C4—122no—
764C3×C4—182no—
765C3×C4—182no—
766Dic3—22no—
767Dic3—62no—
768Dic3—62no—
769Dic3—62no—
770Dic3—62no—
771Dic3—122no—
772Dic3—122no—
773Dic3—182no—
774Dic3—182no—
775Dic3—182no—
776Dic3—362no—
777Dic3—362no—
778Dic3—362no—
779Dic3—722no—
780Dic3C2×D3×Dic312yes—
781Dic3C2×D3×Dic312yes—
782C32—21no—
783C32—21no—
784C32—21no—
785C32—41no—
786C32#548611yescharacteristic, complemented
787C32#552111yescharacteristic, complemented
788C32#579811yescharacteristic, complemented
789C23—31no—
790C23—31no—
791C23—34no—
792C23—91no—
793C23—91no—
794C23—94no—
795C23—122no—
796C23—362no—
797C23D3311yescharacteristic
798D4—94no—
799D4—94no—
800D4—94no—
801D4—94no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—34no—
805C2×C4—32no—
806C2×C4—92no—
807C2×C4—92no—
808C2×C4—272no—
809C2×C4—362no—
810C2×C4—1082no—
811C2×C4—1082no—
812C2×C4—1082no—
813C2×C3—22no—
814C2×C3—22no—
815C2×C3—22no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—22no—
820C2×C3—22no—
821C2×C3—22no—
822C2×C3—42no—
823C2×C3—42no—
824C2×C3—42no—
825C2×C3—41no—
826C2×C3—42no—
827C2×C3—64no—
828C2×C3—62no—
829C2×C3—62no—
830C2×C3—62no—
831C2×C3—62no—
832C2×C3—82no—
833C2×C3—122no—
834C2×C3—182no—
835C2×C3—182no—
836C2×C3C2×C4×D3211yescharacteristic
837C2×C3#6430712yes—
838C2×C3#6431412yes—
839C2×C3C22×D3×Dic311yescharacteristic
840C2×C3C22×D3×Dic311yescharacteristic
841C2×C3#6433012yes—
842D3—22no—
843D3—22no—
844D3—64no—
845D3—62no—
846D3—62no—
847D3—62no—
848D3—62no—
849D3—122no—
850C22—22no—
851C22—32no—
852C22—32no—
853C22—62no—
854C22—62no—
855C22—92no—
856C22—92no—
857C22—124no—
858C22—182no—
859C22—182no—
860C22—364no—
861C22D32×Dic312yes—
862C22C2×D3311yescharacteristic
863C4—32no—
864C4—32no—
865C4—62no—
866C4—182no—
867C4—182no—
868C4—542no—
869C3—21no—
870C3—21no—
871C3—21no—
872C3—41no—
873C3#1059418211yescharacteristic, complemented
874C3#1059498211yescharacteristic, complemented
875C3#1059550611yescharacteristic, complemented
876C2—22no—
877C2—62no—
878C2—62no—
879C2—182no—
880C2—182no—
881C2C2×D32×Dic311yescharacteristic
882C2#1172441812yes—
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC23×C33C23
socle, cosocleC22×C33C24
prime radicalC22×C3×#626C2
hypercenterC23D33
hypocenterC33#518
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11723723C2semidirect
3. C3⋊D3×#217C2semidirect
4. D3×#3757C2semidirect
5. #11723594C2semidirect
6. C3×D3×#217C2semidirect
7. C3×#63955C2semidirect
8. #11722929C2semidirect
9. #11722928C2semidirect
10. #11722927C2semidirect
11. Dic3×#626C2semidirect
18. C2×#6294C22semidirect
19. C2×Dic3×C3⋊D3C22semidirect
20. C2×D3×C3⋊Dic3C22semidirect
21. C2×C3×#626C4semidirect
26. C2×C3×D3×Dic3C22semidirect
31. #88814C22semidirect
32. Dic3⋊(C3⋊Dic3)C22semidirect
33. #88803C22semidirect
34. (C2×D3)⋊(C3⋊Dic3)C22semidirect
35. Dic3×C3⋊Dic3C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
38. C3×Dic32C22semidirect
62. D3×#217D3semidirect
66. #63955D3semidirect
77. C22×C3×C3⋊D3C2×C4semidirect
81. C22×C32×D3C2×C4semidirect
87. C2×C32×Dic3C2×C4semidirect
94. C3×#626C2×C4semidirect
95. C3×#626C2×C4semidirect
96. C3×#626C2×C4semidirect
97. C3×#626C2×C4semidirect
128. C2×#626Dic3semidirect
142. C2×D3×Dic3C2×D3semidirect
175. Dic3⋊Dic3C2×D3semidirect
185. (C2×D3)⋊Dic3C2×D3semidirect
189. Dic32C2×D3semidirect
257. C22×C3⋊D3C2×Dic3semidirect
278. C22×C3×D3C4×D3semidirect
279. C22×C3×D3C2×Dic3semidirect
314. C2×C3×Dic3C4×D3semidirect
315. C2×C3×Dic3C2×Dic3semidirect
327. #626C2×Dic3semidirect
328. #626C2×Dic3semidirect
329. #626C2×Dic3semidirect
330. #626C2×Dic3semidirect
536. C33#518semidirect
573. C22×D3D3×Dic3semidirect
618. C2×Dic3D3×Dic3semidirect
786. C32#5486semidirect
787. C32#5521semidirect
788. C32#5798semidirect
873. C3#10594182semidirect
874. C3#10594982semidirect
875. C3#10595506semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×#6262
#117237232
C3⋊D3×#2172
D3×#37572
#117235942
C3×D3×#2172
C3×#639552
#117229292
#117229282
#117229272
Dic3×#6262
#105955063
#105949823
#105941823